Symmetry broken and unbroken solutions of nonlocal NLS equation in 2+1 dimensions

Abstract

In this paper, we study a general nonlinear Schrödinger (NLS) equation in 2+1 dimensions which under appropriate nonlocal symmetry reduction leads to reverse space nonlocal NLS equation. We apply Darboux transformation and construct multiple solutions of NLS equation in 2+1 dimensions which are expressed in terms of quasideterminants. Under suitable reductions the quasideterminant formula empowers us to compute explicit expressions of symmetry broken and symmetry unbroken solutions of a generic NLS equation and PT-symmetric reverse space nonlocal NLS equation in 2+1 dimensions respectively. Furthermore the dynamics of symmetry broken and symmetry unbroken first two nontrivial solutions are presented. Under the dimensional reduction we obtain first- and second-order nontrivial solutions of 1+1-dimensional nonlocal NLS equation. By applying local symmetry reduction, we obtain one- and two-soliton solutions of 2+1-dimensional local NLS equation.

Keywords

• Reverse space nonlocal nonlinear Schrödinger (NLS) equation in 2+1 dimensions
• Darboux transformation (DT)
• Quasideterminants
• Symmetry unbroken and broken solutions